First slide

Motion of planets and satellites

Question

A space ship is launched into a circular orbit close to the surface of the earth. The additional velocity now imparted to the spaceship in the orbit to overcome the gravitational pull is

Moderate

A

$11.2 {kms}^{- 1}$
B

$8 {kms}^{- 1}$
C

$3.2 {kms}^{- 1}$
D

$1.414 \times 8 {kms}^{- 1}$

Solution

$\begin{array}{l} v_{e} = 11 .2 km / s \\ \frac{{mv}^{' 2}}{R} = \frac{GMm}{R^{2}} \\ v^{' 2} = \frac{GM}{R^{2}} R = 8 km / s \end{array}$
Therefore, the additional velocity $= (11.2 - 8) = 3.2 km / s$

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